Little Bits of Artificial Intelligence

1. Story Analogy: “Chef Neuron in a Hidden Kitchen”

Imagine we’re in a restaurant kitchen (the hidden layer) and each chef (neuron) is trying to prepare a special dish based on ingredients (inputs) they get.

Each chef:

1. Receives different amounts of each ingredient (weights).
2. Mixes them (weighted sum).
3. Adds a secret spice (bias).
4. Tastes it and decides if it’s spicy enough to serve (activation function).

Each chef’s decision becomes the output passed to the next kitchen (layer).

2. Mathematical Structure of a Neuron

A neuron receives multiple inputs and calculates an output using:

Then applies an activation function (like sigmoid, ReLU): a=σ(z)

Example with 3 inputs:

z=0.2⋅x1+(−0.5)⋅x2+1.0⋅x3+0.1

a=ReLU(z)=max(0,z)

In a Hidden Layer : If the hidden layer has 4 neurons, each neuron does the above process independently, and produces its own activation output.

These 4 outputs then move to the next layer (possibly another hidden layer or the output layer).

3. Story Analogy Continued: From Hidden Chefs to Final Dish

From our earlier kitchen story:

• We had 3 chefs (neurons in the hidden layer) who each made a sauce.
• Now, a head chef (output neuron) tastes all three sauces, mixes them with a unique recipe (new weights), adds a final spice (bias), and decides the final taste (prediction).

4. Mathematical Structure of Output from Hidden Layer

Let’s say our hidden layer gives:

H1,h2,h3 (these are outputs from hidden neurons)

The output neuron will compute:

Then apply an activation function:

• For regression → use linear or identity function (just return z)
• For binary classification → use sigmoid
• For multi-class classification → use softmax